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Invariants related to the tree property

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Abstract

We consider cardinal invariants related to Shelah’s model-theoretic tree properties and the relations that obtain between them. From strong colorings, we construct theories T with κcdt(T) > κsct(T) + κinp(T). We show that these invariants have distinct structural consequences, by investigating their effect on the decay of saturation in ultrapowers. This answers some questions of Shelah.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, Berkeley, CA, 94720-3840, USA

    Nicholas Ramsey

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  1. Nicholas Ramsey
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Correspondence to Nicholas Ramsey.

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Ramsey, N. Invariants related to the tree property. Isr. J. Math. 240, 275–314 (2020). https://doi.org/10.1007/s11856-020-2066-0

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  • DOI: https://doi.org/10.1007/s11856-020-2066-0

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